Subgroups — C₃×C₇×C₂₅×C₆₁ #44545045

Order 32025.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₂₅×C₆₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₃×C₅×C₇×C₆₁	C₅	1	1	yes	maximal, characteristic
3	C₃×C₂₅×C₆₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₇×C₆₁	C₃×C₅	1	1	yes	characteristic
5	C₂₅×C₆₁	C₃×C₇	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₇×C₆₁	C₂₅	1	1	yes	characteristic, direct product factor, Hall
7	C₃×C₅×C₆₁	C₅×C₇	1	1	yes	characteristic
8	C₃×C₇×C₂₅	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₇×C₆₁	C₃×C₂₅	1	1	yes	characteristic, direct product factor, Hall
10	C₅×C₆₁	C₃×C₅×C₇	1	1	yes	characteristic
11	C₃×C₆₁	C₇×C₂₅	1	1	yes	characteristic, direct product factor, Hall
12	C₇×C₂₅	C₃×C₆₁	1	1	yes	characteristic, direct product factor, Hall
13	C₃×C₅×C₇	C₅×C₆₁	1	1	yes	characteristic
14	C₃×C₂₅	C₇×C₆₁	1	1	yes	characteristic, direct product factor, Hall
15	C₆₁	C₃×C₇×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
16	C₅×C₇	C₃×C₅×C₆₁	1	1	yes	characteristic
17	C₂₅	C₃×C₇×C₆₁	1	1	yes	characteristic, direct product factor, Sylow
18	C₃×C₇	C₂₅×C₆₁	1	1	yes	characteristic, direct product factor, Hall
19	C₃×C₅	C₅×C₇×C₆₁	1	1	yes	characteristic
20	C₇	C₃×C₂₅×C₆₁	1	1	yes	characteristic, direct product factor, Sylow
21	C₅	C₃×C₅×C₇×C₆₁	1	1	yes	characteristic
22	C₃	C₇×C₂₅×C₆₁	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₅	C₃×C₅×C₇×C₆₁
socle, prime radical	C₃×C₅×C₇×C₆₁	C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₇×C₂₅×C₆₁	C₃	direct (N × H)
3. C₃×C₂₅×C₆₁	C₇	direct (N × H)
5. C₂₅×C₆₁	C₃×C₇	direct (N × H)
6. C₃×C₇×C₆₁	C₂₅	direct (N × H)
8. C₃×C₇×C₂₅	C₆₁	direct (N × H)
9. C₇×C₆₁	C₃×C₂₅	direct (N × H)
11. C₃×C₆₁	C₇×C₂₅	direct (N × H)
12. C₇×C₂₅	C₃×C₆₁	direct (N × H)
14. C₃×C₂₅	C₇×C₆₁	direct (N × H)
15. C₆₁	C₃×C₇×C₂₅	direct (N × H)
17. C₂₅	C₃×C₇×C₆₁	direct (N × H)
18. C₃×C₇	C₂₅×C₆₁	direct (N × H)
20. C₇	C₃×C₂₅×C₆₁	direct (N × H)
22. C₃	C₇×C₂₅×C₆₁	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₇×C₂₅×C₆₁	3
C₃×C₅×C₇×C₆₁	5
C₃×C₂₅×C₆₁	7
C₃×C₇×C₂₅	61

Subgroups — C3×C7×C25×C61 #44545045

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇×C₂₅×C₆₁ #44545045